Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...

Newton’s Method

Newton’s Method

Newton’s Method is a powerful iterative technique for approximating the roots of real-valued, differentiable functions, particularly when analytical solutions are impractical. This approach is widely used in scientific computing, engineering, and finance, where equations may be too complex for traditional algebraic methods to handle. The method relies on an iterative process that refines an initial estimate using the function’s derivative to approach the true solution progressively.

Linearization and Approximation

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...

Statically Indeterminate Problem Solving

Statically Indeterminate Problem Solving

Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining...

Trigonometric Substitution

Trigonometric Substitution

Trigonometric substitution is a technique used to simplify integrals that contain square root expressions involving quadratic forms. It is particularly effective when the integrand includes terms resembling those found in standard geometric equations, such as circles or ellipses.Molniya satellites follow highly elliptical orbits, repeatedly sweeping out the same regions of space as they revolve around Earth. To estimate the area enclosed by such an orbit, the path is modeled as an ellipse...

Implicit Differentiation: Problem Solving

Implicit Differentiation: Problem Solving

Curves defined implicitly, where variables cannot be separated algebraically, require specialized techniques for analysis. The conchoid of Nicomedes exemplifies such a case. Its equation links x and y in a way that prevents isolation of one variable, making implicit differentiation essential to determine the slope and behavior at any point on the curve.The implicit form of the conchoid can be expressed as:To differentiate this equation, y is treated as a function of x, and the chain rule is...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Suppression of macrophage enriched miRNA 210-3p improves cardiac fibrosis and cardiac function following myocardial infarction.

Clinical hemorheology and microcirculation·2026

Same author

A proof-of-concept automated method for accurate skin dosimetry: correcting overestimated surface dose measurements.

Physics in medicine and biology·2026

Same author

Comparative analysis of radiation therapy plans before and after biodegradable hydrogel (SpaceOAR) injection for reducing rectal toxicity in patients with prostate cancer undergoing carbon ion radiotherapy.

Frontiers in oncology·2026

Same author

Development and validation of an automated, accurate in-house treatment planning system for pencil-beam scanning carbon ion radiotherapy.

Medical physics·2026

Same author

Proangiogenic and Collagen-Promoting Effects of a 70% Ethanol Extract of <i>Grateloupia angusta</i> in Cutaneous Wound Models.

International journal of molecular sciences·2026

Same author

Jamming and Yielding in Dense Suspensions.

Annual review of chemical and biomolecular engineering·2026

Search research articles

Related Experiment Video

Updated: May 21, 2026

Proton Therapy Delivery and Its Clinical Application in Select Solid Tumor Malignancies

Proton Therapy Delivery and Its Clinical Application in Select Solid Tumor Malignancies

Published on: February 6, 2019

Efficient IMRT inverse planning with a new L1-solver: template for first-order conic solver.

Hojin Kim¹, Tae-Suk Suh, Rena Lee

¹Department of Radiation Oncology, Stanford University, Stanford, CA 94305, USA.

Physics in Medicine and Biology

|June 12, 2012

Summary

This study introduces a faster, memory-efficient method for Intensity Modulated Radiation Therapy (IMRT) inverse planning using the Template for First-Order Conic Solver (TFOCS) algorithm. TFOCS significantly speeds up calculations and reduces memory use compared to traditional Quadratic Programming methods.

More Related Videos

Radiation Planning Assistant - A Web-based Tool to Support High-quality Radiotherapy in Clinics with Limited Resources

Radiation Planning Assistant - A Web-based Tool to Support High-quality Radiotherapy in Clinics with Limited Resources

Published on: October 6, 2023

Radiation Planning Assistant - A Streamlined, Fully Automated Radiotherapy Treatment Planning System

Radiation Planning Assistant - A Streamlined, Fully Automated Radiotherapy Treatment Planning System

Published on: April 11, 2018

Related Experiment Videos

Last Updated: May 21, 2026

Proton Therapy Delivery and Its Clinical Application in Select Solid Tumor Malignancies

Proton Therapy Delivery and Its Clinical Application in Select Solid Tumor Malignancies

Published on: February 6, 2019

Radiation Planning Assistant - A Web-based Tool to Support High-quality Radiotherapy in Clinics with Limited Resources

Radiation Planning Assistant - A Web-based Tool to Support High-quality Radiotherapy in Clinics with Limited Resources

Published on: October 6, 2023

Radiation Planning Assistant - A Streamlined, Fully Automated Radiotherapy Treatment Planning System

Radiation Planning Assistant - A Streamlined, Fully Automated Radiotherapy Treatment Planning System

Published on: April 11, 2018

Area of Science:

Medical Physics
Radiation Oncology
Computational Optimization

Background:

Intensity modulated radiation therapy (IMRT) inverse planning aims to simplify fluence maps for better dose delivery.
Traditional optimization methods like Quadratic Programming (QP) for total-variation (TV) regularization are computationally intensive and memory-demanding.

Purpose of the Study:

To introduce and evaluate the Template for First-Order Conic Solver (TFOCS) as a fast and memory-efficient alternative for IMRT inverse planning.
To compare the performance of TFOCS against conventional QP-based methods in clinical IMRT scenarios.

Main Methods:

Implemented TFOCS, a first-order algorithm, for TV minimization in IMRT inverse planning, avoiding the need for Hessian matrix computation.
Evaluated TFOCS and QP methods on head and neck and prostate cancer cases, ensuring comparable dose conformity for fair comparison.

Main Results:

TFOCS demonstrated a significant improvement in computational efficiency for fluence map optimization.
The TFOCS-based method achieved 4-6 times faster computation and 3-4 times lower memory requirements compared to QP.
Conformal dose distributions were maintained with the TFOCS approach.

Conclusions:

TFOCS offers an effective, fast, and memory-efficient solution for IMRT inverse planning.
This method is particularly advantageous for complex planning scenarios involving numerous beams, such as VMAT and DASSIM-RT.